Here’s a link to the 2014 Ph.D. thesis of Jason Miller, Okounkov Bodies of Borel Orbit Closures in Wonderful Group Compactifications.
This is a reading and viewing list for a small group of people who are working to learn these topics. Anyone is welcome to use it, of course.
- Algebraic groups and representation theory
- Humphreys, Linear Algebraic Groups (Springer)
- Toric varieties
- Cox, Little, Schenck, Toric varieties (AMS)
- Tropical geometry
- Spherical varieties
- Associated convex bodies
- Lazarsfeld and Mustaţă, Convex Bodies Associated to Linear Series, (arXiv:0805.4559)
- Kaveh and Khovanskii, Convex bodies associated to actions of reductive groups, (arXiv:1001.4830)
- Kiritchenko, Smirnov, Timorin, Schubert calculus and Gelfand-Zetlin polytopes, (arXiv: 1101.0278)
- Miller, Okounkov Bodies of Borel Orbit Closures in Wonderful Group Compactifications, Ph.D. dissertation at the Ohio State University, 2014
- Videos from the workshop Convex Bodies and Representation Theory at the Banff International Research Station in February 2014